**Dates:** July 6– 17, 2019 (see calendar below for details please)

**Location:** Classes will be held at **Harvard University** in Cambridge, MA

Residential Students will stay at Harvard Square.

**Ages:** 11-18 for residential students, 9-18 for day students.

**Tuition:** $1,885 for day campers, $4,450 for residential students. ($250 deposit paid at the time of registration, full tuition is dude April 30th)

Please scroll down for more information.

**Master Math!**

CyberMath Academy’s **Summer Math Camp** in Boston, MA is a selective summer program for students who would like to sharpen their math skills in the inspiring and motivating atmosphere of an Ivy League College. Our camp provides a challenging environment for students in which they master mathematics with the participation of brilliant students from all over the globe.

**Advanced Math Program – Designed by Justin Stevens**

“- Author of Olympiad Number Theory Through Challenging Problems Book

– “Our teacher, Justin, was a legend.” 2018 Camp Participant

– “Justin is a crazy good teacher and understands kids.” 2018 Camp Participant

– “Justin is the most awesome teacher EVER!!!’ 2018 Camp Participant”

“Math Olympiad Program – Designed by Evan Chen

– One of the coaches of the USA IMO Team

– Co-Exam Coordinator for the USA Olympiad Team Selection Tests

– Assistant Academic Director of the Math Olympiad Summer Program (MOP)

– Member of the USA Math Olympiad (USAMO) Committee”

**Courses to Choose From and Who This Camp is For**

**1- Students who would like to excel in school mathematics**

Courses to choose from:

###### Advanced Middle School Math with MathCounts/AMC 8-10 Problems

*This course covers the main topics in middle school math. Students will be mastering these topics while solving challenging problems at the level of or from MathCounts, AMC-8, AMC 10 and similar competitions. Students go above and beyond Common Core standards in this brain-stimulating course. Students will also solve mathematical puzzles and cyphers and learn topics that are typically not covered at traditional school settings.***Recommended Grade Levels:**Although we do not limit students by grade level, this course is typically recommended for students in grades 4th-8th.**Course Description:**This course will familiarize students with the essential concepts and techniques in Pre-Algebra, Algebra I, Geometry, Number Theory and Combinatorics. We will have a specific emphasis on problem solving where the students will constantly be challenged to think creatively.**Contest Preparation:**MathCounts, AMC 8, AMC 10.**Course Objectives:**As of the completion of this course, students will:1. Have complete mastery of concepts covered in standard Pre-Algebra, Algebra I and Geometry courses, as well as topics not covered in traditional school curriculum.

2. Be able to explain and employ important theorems and techniques used in Combinatorics, Number Theory, and Geometry.

3. Be able to reduce unfamiliar problems to basic principles, and cleverly employ techniques they’ve learned to find shortcuts in solution methods.

**Teaching Philosophy:**We believe that building good problem-solving skills is as (if not more) important than knowing lots of theorems. As such, although the course will cover a considerable amount of material, the main emphasis will be on building problem-solving intuition and training students to think creatively when faced with classes of problems they’ve never seen before.**Class Participation:**Students are expected to actively participate in class. We will employ the Socrates method, which is a cooperative dialogue between the students and teacher to stimulate critical thinking. Students will also collaborate with classmates while solving challenging problems.**Curriculum:**The course curriculum is owned and copyright by CyberMath Academy. The class material is composed of unique blends of problems hand picked from prestigious competitions from around the globe, along with many historical problems and fascinating puzzles.**Information on Summer Camp Attendance Options (Academic Year Courses cover all topics)****Full-Day Program:**Students who would like to master all topics should register for full-day program**Half-Day Program:**Students who would like to master only Pre-Algebra and ALgebra-I topics alongside Number Theory can choose this option. Students can also choose to enroll only in morning classes.**Algebra**• Ratios and Proportions

• Algebraic Expressions

• Linear Equations

• Functions

• Inequalities

• Polynomial Expressions

• Pascal’s Triangle

• Binomial Theorem

• Quadratic Equations**Combinatorics**• Counting

• Statistics

• Probability

• Permutations

• Combinations**Number Theory**• Divisibility

• GCD and LCM

• Prime Factorization

• Radicals and Exponents

• Modular Arithmetic

• Sequences and Series

• Gauss’s Formula**Geometry**• Angles

• Triangles

• Pythagorean Theorem

• Polygons

• Circles

• Perimeter, Area and Volume

• Coordinate Geometry

• 3D Geometry

###### Advanced High School Math with AMC 10/12 Problems

*This course prepares students for American Mathematics Competitions 10 and 12 and the non-proof parts of AIME. The topics taught include***the entire high school curriculum including trigonometry, advanced algebra, precalculus and advanced geometry,**but exclude calculus. Our curriculum also includes some additional challenging and brain-stimulating topics outside of the traditional school curriculum.**Recommended Grade Levels:**Although we do not limit students by grade level, this course is typically recommended for advanced 7th and 8th graders and high school students.**Course Description:**This course will familiarize students with the essential concepts and techniques in Algebra II, PreCalculus, Combinatorics, Number Theory, and Geometry. We will have a specific emphasis on problem solving where the students will constantly be challenged to think creatively.**Contest Preparation:**AMC 10/12, AIME, ARML, Mandelbrot, Purple Comet.**Course Objectives:**As of the completion of this course, students will:1. Have complete mastery of concepts covered in standard Algebra II and PreCalculus courses, as well as more advanced topics (such as Vieta’s formulas, Complex Numbers, and manipulation of Series).

2. Be able to explain and employ important theorems and techniques used in Combinatorics, Number Theory, and Geometry.

3. Be able to reduce unfamiliar problems to basic principles, and cleverly employ techniques they’ve learned to find shortcuts in solution methods.

**Teaching Philosophy:**We believe that building good problem-solving skills is as (if not more) important than knowing lots of theorems. As such, although the course will cover a considerable amount of material, the main emphasis will be on building problem-solving intuition and training students to think creatively when faced with classes of problems they’ve never seen before.**Class Participation:**Students are expected to actively participate in class. We will employ the Socrates method, which is a cooperative dialogue between the students and teacher to stimulate critical thinking. Students will also collaborate with classmates while solving challenging problems.**Curriculum:**The course curriculum is owned and copyright by CyberMath Academy. The class material is composed of unique blends of problems hand picked from prestigious competitions from around the globe, along with many historical problems and fascinating puzzles.**Information on Summer Camp Attendance Options (Academic Year Courses cover all topics)****Full-Day Program:**Students who would like to master all topics should register for full-day program**Half-Day Program:**Students who would like to master only Algebra II or PreCalculus topics alongside Number Theory can choose this option. Students can also choose to enroll only in morning classes.**Topics Covered In This Course****Algebra**– Quadratics/Discriminants & Conic Sections

– System of Equations

– Polynomial Division

– Rational Root Theorem

– Fundamental Theorem of Algebra

– Vieta’s Formulas

– Sequences and Series

– Induction

– Radicals and Rationalizing Denominators

– Algebraic Factorizations

– Complex Numbers

– Inequalities

– Functions

– Exponents and Logarithms**Combinatorics**– Basic Counting: Constructive and Complimentary

– Sets, Bijections, and Logic

– Principle of Inclusion Exclusion

– Combinations and Permutations

– Pascal’s Triangle

– Binomial Theorem

– Combinatorial Identities

– Pigeonhole Principle

– Expected Value

– Stars & Bars

– Recursion

– Fibonacci Numbers**Number Theory**– Prime Factorization

– Divisibility Rules

– Euclidean Algorithm

– Diophantine Equations

– Bezout’s Identity

– Modular Arithmetic & Exponentiation

– Fermat’s Little Theorem

– Wilson’s Theorem

– Chinese Remainder Theorem

– Multiplicative Functions

– Euler’s Theorem**Geometry**– Congruent & Similar Triangles

– Special Parts of a Triangle

– Triangle Area Formulas

– Quadrilaterals

– Angles in Polygons

– Inscribed Angles in Circles

– Power of a Point

– Three-Dimensional Geometry

– Trigonometry for Right Triangles

– Unit Circle & Radians

– Trigonometric Identities

– Extended Law of Sines & Law of Cosines

– Polar Coordinates & Geometry of Complex Numbers**Click below to see sample lecture notes****AUTHORS****Justin Stevens:**Accelerated Math Program Coordinator

University of Alberta – jstevens@cybermath.academy – (909) 713-4398**Forest Kobayashi:**Curriculum Designer, Harvey Mudd College**Alex Toller:**Curriculum Designer

If you would like to get more information on AMC 8, 10, 12 and AIME competitions, please visit Mathematical Association of America’s American Mathematics Competitions (AMC) Page.

**2- Students who would like to go above and beyond school mathematics**

Courses to choose from:

– Proof Mathematics with AIME Problems

This course is a part of our Math Olympiad Program. You can find more information about our Math Olympiad Program below.

###### Math Olympiad Program Levels

To find out what course is best for you, please look at the information below:

There are two tracks in this course:

**Proof Mathematics with AIME Problems**For students who can comfortably qualify for the

AIME and solve the first half of problems on the exam. These students might be

aiming to qualify for USA(J)MO and have a pleasant start on the olympiad.**USA(J)MO:**For students who can already comfortably qualify for USA(J)MO, and

are aiming to score highly on it.**First: Please determine your level below**(1) Starting out on AMC, trying to qualify for AIME

(2) Can solve 2 problems on AIME, hoping to solve 8

(3) Can solve 6+ problems on AIME, hoping to solve 13

(4) Can qualify for USA(J)MO, hoping to solve a problem or two

(5) Can solve one or two USA(J)MO problems and solve hard USAJMO or medium USAMO problems

(6) Aiming to solve the final P3 / P6 problems on USAMO

**Second:Learn about the tracks in our Math Olympiad Program**Our Math Olympiad Program has two tracks:

*Entry Level Math Olympiad Course with Computations (Advanced AIME with Proofs)** Prerequisites: 6+ on AIME

* Aiming for high AIME scores, and a couple problems on USA(J)MO

*Advanced Math Olympiad Course (USAJMO)** Prerequisites: consistently qualify for USA(J)MO

* Aiming to score 14+ on USAMO

**Third: Placement**– If you are in levels 1 or 2, you should sign up for our Advanced High School Math with AMC 10/12 Problems course. It covers AMC 10/12 and the non-proof problems on AIME.

– If you are in levels 3 or 4, you should sign up for our Advanced AIME with Proofs course.

– If you are in levels 5 or 6, you should sign up for our USA(J)MO course.

Have questions? E-mail our Math Olympiad Program Coordinator Evan Chen at echen@cybermath.academy

###### Math Olympiad Program Curriculum

There are two tracks in this program:

**Advanced AIME with Proofs:**For students who can comfortably qualify for the

AIME and solve the first half of problems on the exam. These students might be

aiming to qualify for USA(J)MO and have a pleasant start on the olympiad.**USA(J)MO:**For students who can already comfortably qualify for USA(J)MO, and

are aiming to score highly on it.These two tracks overlap in any given year. The curriculum runs in a three-year cycle.

**Contest preparation:**AIME, HMMT, USA(J)MO, IMO.**Curriculum:**The course operates on a three-year cycle, so students can repeat the course up to three times total, across both tracks. The summer and year-round materials

are disjoint.A detailed listing of topics covered appears below. Not all topics occur in all years. Most topics occur in multiple years, but they will have different examples and problems each time they appear over the three-year cycle.

Each iteration of the course contains several practice exams.

**1- Topics appearing only in Advanced AIME with Proofs****Algebra***Symmetric Polynomials.*Vieta’s formulas, Newton sums, fundamental theorem of elementary symmetric polynomials.*Logarithms.*Computational problems and equations involving logarithms.*Trig Equation.*Algebraic problems involving trig functions.*Intro Functional Equation.*Introduction to olympiad-style functional equations. Substitutions, injectivity and surjectivity, Cauchy’s functional equation.*Inequalities.*Introduction to olympiad-style inequalities. AM-GM and Cauchy-Schwarz.

**Combinatorics***Computations with Probability.*Random variables, expected value, linearity of expectation.*Enumeration.*Computational counting problems.- Monovariants and Invariants.
*Finite processes.*

*Computational Geometry.*AIME-style problems in Euclidean geometry.

Angle Chasing.*Trig in Geometry.**Elementary Geometry.*Angle chasing, power of a point, homothety.*Basics of Complex Numbers. Introduction to complex numbers in geometry.*

**Number theory***Computations with Modular Arithmetic.*Fermat, Wilson, Chinese Remainder theorem.*Diophantine Equations.*Introduction to olympiad-style Diophantine equations.*Chinese Remainder Theorem.*

**2- Topics appearing in both tracks****Algebra***Generating Functions.*Their uses in combinatorial sums.*Linear Recursions and Finite Differences.**Sums.*Swapping order of summation.*Polynomials.*Fundamental theorem of algebra, factorizations, roots.

**Combinatorics***Weights and Colorings.**Induction and Recursion.**Linearity of Expectation and Double-Counting.**Algorithms.*Combinatorial problems involving discrete-time processes.*Graph Theory.*Definitions and problems.*Ad-Hoc Constructions.**Problems on Rectangular Grids.*

**Geometry***Power of a Point.**Homothety**Common Congurations.*

**Number theory***Divisibility and Euclidean Algorithm.*Bounding the remainders.*Look at the Exponent.*p-adic evaluation, lifting the exponent.*Orders. Primes of the form a2 + b2.*Primitive roots.

**3- Topics appearing only in USA(J)MO****Algebra***Functional Equations.*More diffi cult functional equations at the USAMO/IMO level.*Advanced Inequalities.*Jensen and Schur. Fudging, smoothing.*Analysis and Calculus.*Understanding the complete theorem statements in calculus and how they can be applied to olympiad problems. Differentiation and the relation

to multiplicity of roots. Lagrange multipliers. Compactness.

**Combinatorics***Advanced Graph Theory.*More di fficult olympiad problems involving graphs.*Advanced Algorithms.**Games and Processes.*

**Geometry***Projective Geometry.*Harmonic bundles, poles and polars.*Inversion.**Spiral Similarity.**Complex Numbers.*Applications to problems.*Barycentric Coordinates.*Applications to problems.

**Number theory***Constructions in Number Theory.**Integer Polynomials.*Irreducibility, minimal polynomials, a taste of Galois theory.*Quadratic Reciprocity.*Legendre symbols.

**Distribution of Math Strands**

**Morning Sessions:** Combinatorics and Geometry topics will be covered.

**Afternoon Sessions:** Algebra and Number Theory topics will be covered.

**Outstanding Teachers!**

Please see our faculty page for our instructors. Summer Math Camp instructors will be some of the instructors listed on our faculty page or other outstanding teachers with similar credentials.

**Guest Lectures by Harvard, MIT Researchers**

TBA.

The guest lectures will be held at the 250-year old courtroom on the first day of the camp.

**Students’ Forum**

There will be two student forums for our students:

**Students’ Forum 1:** Learn how to get accepted to top colleges from students who currently attend Harvard, MIT and other top colleges.

**Students’ Forum 2:** Learn how to prepare for math competitions and olympiads from champions who aced these tests.

**Harvard, MIT Campus Tours and Lab Visits**

Harvard and MIT Campus Tours and laboratory visits are scheduled each year.

**Sightseeing**

We will visit the historical places to see first-hand where the United States was founded and learn about its history. Walk along The Freedom Trail, try many tastes at Quincy Market, when tired of walking hop on a Duck Tour and take a walk along Charles River. Feel smarter (pronounced SMAHTAH) at Harvard Square.

**Schedule of Activities**

Date | Morning | Afternoon |
---|---|---|

Fri, July 5 | Residential and Int. Students Arrive | Orientation, Time at Harvard Square |

Sat, July 6 | Opening,Placement Tests & Guest Lecture | Math Classes |

Sun, July 7 | Math Classes | Math Classes |

Mon, July 8 | Math Classes | Math Classes |

Tue, July 9 | Math Classes | Math Classes |

Wed, July 10 | Math Classes | Math Classes |

Thu, July 11 | Harvard Campus Tour, Students’ Forum | MIT Campus Tour |

Fri, July 12 | Math Classes | Math Classes |

Sat, July 13 | Math Classes | Math Classes |

Sun, July 14 | Math Classes | Math Classes |

Mon, July 15 | Math Classes | Math Classes |

Tue, July 16 | Math Classes | Math Classes |

Wed, July 17 | Math Classes | Practice Test, Award Ceremony |

Domestic Residential Students Depart | ||

Thu, July 18 | Academic Counseling for Int. Students | Study Planning for Int. Students |

Fri, July 19 | International Students Depart | |

**Optional Additional East Coast Trip**

This optional program is a wonderful opportunity for students who would like to have an eye-opening and awe-inspiring experience visiting the top academic and touristic destinations in the East Coast of the United States. Many international students as well as domestic ones would like to breathe the motivating air in these world renowned places and experience first-hand what makes them great. Please note that this is an optional program in addition to our regular summer camp program and requires an additional fee of $3,850. This fee covers everything including transportation, meals, accommodation, applicable entrance fees for museums and other attractions.

Date | Morning | Afternoon |
---|---|---|

Fri, July 19 | Harvard Admissions Information, Scientists’ Forum | MIT & Kendall Square Labs Tour |

Sat, July 20 | Greater Boston Area Tour | Greater Boston Area Boat Tour |

Sun, July 21 | Yale University Campus Tour | Yale University Admissions Session |

Mon, July 22 | New York City Tour | New York City Boat Tour |

Tue, July 23 | American Museum of Natural History, The Metropolitan Museum of Art | Columbia University Tour |

Wed, July 24 | Shopping Mall: Outlet Stores | Students Depart |

**Daily Schedule**

Time | Activity | Notes |
---|---|---|

7:15 am – 8:15 am | Breakfast | Residential Students Only |

8:15 am – 8:45 am | Day students arrive | |

9:00 am – 12:15 pm | Morning classes | |

12:15 pm – 1:15 pm | Lunch and Activity time | Conversation with teachers/counselors |

1:15 pm – 4:30 pm | Afternoon classes | |

4:30 pm – 5:00 pm | Day students depart | |

5:00 pm – 6:00 pm | Free time | Residential Students Only* |

6:00 pm – 7:15 pm | Dinner | Residential Students Only* |

7:30 pm – 9:30 pm | Study Time | Residential Students Only* |

9:30 pm – 10:30 pm | Free Time | Residential Students Only |

10:45 pm | Lights Out | Residential Students Only |

*Day students who wish to attend supervised evening recreational and academic activities at the residential program may do so for an additional fee. The cost will be $200 (including dinner and all activities).

**Transportation**

**Bus Service for Day Students**

We offer bus transportation to our camp site if enough number of students sign up for our Summer Math Camp as day students from the cities listed below. Extra charge will apply and space is limited.

For day students, we provide buses from the following cities: Acton, Lexington, Weston, and Newton

**Airport Pickup**

Domestic residential and international students who will be staying with us overnight at our summer math camp are expected to arrive at Boston Logan International Airport or at the camp site between 7 am – 7 pm on July 5th. For tuition and fees, please see below.

**Tuitions and Deadlines**

**Deposit:** A $250 non-refundable deposit will be requested at the time of registration if the student is admitted. The remaining balance will be due April 30th.

Tuition Type | Deadline | Day Student | Residential Student |
---|---|---|---|

Super Early Bird | November 1st | $1,650 | $3,910 |

Early Registration | April 1st | $1,875 | $4,450 |

Regular Registration | June 1st | $1,975 | $4,700 |

Late Registration | July 14th | $2,175 | $4,950 |

Residential Tuition covers classes & teaching materials, activities, accommodation, meals and in-camp transportation.

**Fees**

International Students’ Fee: Additional $585.

Airport Pickup/Dropoff fee: $60 each

Lunch Fee for Day Students: $232 (Day Students might choose to bring their own lunch or purchase lunch at the University.)

Optional East Coast / Silicon Valley Program Fee: $3,850

**You can save up to $790 by registering early!**